On Wed, 04 Nov 2015 18:12:40 -0500, wrote:

He also needs to check the voltage across the transformer secondary
with the furnace running.to be sure the trasformer is not weak (which
is my suspision.

He can get another transformer connect it to an old appliance cord, add
a few wirenuts, and connect the thermostat wires to it at the furnace.
Then just plug it in to do the test. That saves having to remove the old
one and all of that. Of course if it's determined that the transformer
is faulty, then wire the new one properly.